EXCHANGE 


Capillary  Phenomena  and 
Supercooling 


A  DISSERTATION 

SUBMITTED  IN  PARTIAL  FULFILLMENT  OF  THE  REQUIREMENTS 

FOR  THE  DEGREE  OF  DOCTOR  OF  PHILOSOPHY  IN 

THE  UNIVERSITY  OF  MICHIGAN 


BY 


EDWARD  A.  RYKENBOER 


EASTON,  PA.: 

ESCHBNBACH  PRINTING  Co. 
1917 


Capillary  Phenomena  and 
Supercooling 


A  DISSERTATION 


SUBMITTED  IN  PARTIAL  FULFILLMENT  OF  THE  REQUIREMENTS 

FOR  THE  DEGREE  OF  DOCTOR  OF  PHILOSOPHY  IN 

THE  UNIVERSITY  OF  MICHIGAN 


BY 

EDWARD  A.  RYKENBOER 


EASTON,  PA.: 

ESCHENBACH  PRINTING  Co. 
1917 


JL 


TABLE  OF  CONTENTS. 


Acknowledgment 4 

Part  I. 

Supercooling  in  Capillary  Tubes: 

Introduction 5 

Discussion  of  Supercooling 6 

Subject  of  Investigation 14 

Method  and  Apparatus 15 

Results 21 

Interpretation  of  Results 26 

Influence  of  Variation  in  Experimental  Method:  • 

Variation  in  Rate  of  Cooling 29 

Variation  in  the  Material  of  Which  the  Tube  Is  Made 30 

Part  II. 

Effect  upon  the  Supercooling  of  the  Molecular  Aggregation  of  the  Material 
in  the  Liquid  State: 

Introduction 32 

Chemistry  of  Molten  Sulphur 33 

Influence  of  Foreign  Material  upon  the  Formation  of  Crystallization 

Nuclei 35 

Method  and  Results 36 

.  Interpretation  of  Results 41 

Conclusions „ 43 


ACKNOWLEDGMENT. 

To  Professor  S.  Lawrence  Bigelow,  for  his  instruction  and 
guidance  throughout  this  investigation  and  for  his  helpful 
criticism  of  the  dissertation,  sincere  thanks  are  offered  by  the 
author. 

To  Professor  Edward  H.  Kraus,  for  his  interest  in  the 
dissertation  and  for  class-room  instruction,  thanks  are  also  due. 

The  author  also  wishes  to  express  his  appreciation  to 
Professors  William  D.  Henderson,  Floyd  E.  Bartell,  Harrison 
McAllister  Randall,  Walter  F.  Hunt  and  Dr.  James  E.  Harris, 
for  their  instruction  and  suggestions  in  both  class-room  and 
laboratory. 


CAPILLARY  PHENOMENA  AND  SUPERCOOLING1 


PART  I— SUPERCOOLING  IN  CAPILLARY  TUBES 
Introduction 

In  mountainous  regions  the  existence,  at  a  definite  alti- 
tude, of  a  clearly  marked  "tree  line,"  indicates  that  above 
this  the  average  temperature  is  too  low  for  the  trees  to  with- 
stand. Certain  forms  of  vegetation  cannot  survive  the  winter 
above  certain  latitudes.  It  would  appear  to  be  a  logical  con- 
clusion that  the  completeness  with  which  all  moisture  within 
the  tree  or  plant  is  frozen  is  at  least  one  factor  determining 
whether  it  lives  or  dies. 

Under  certain  conditions  liquids  may  be  supercooled  many 
degrees  below  their  freezing  points  without  solidification.  It 
occurred  to  us  that  sufficient  smallness  of  cells  or  capillary 
tubes  might  make  possible  a  degree  of  supercooling  such  that 
at  least  some  of  the  contained  moisture  did  not  freeze  and 
that  this  might  be  the  reason  that  some  plants  or  trees  were  not 
"winter  killed,"  but  resumed  their  growth  in  the  spring. 
In  winter,  trees  and  plants  are  frequently  subjected  to  tempera- 
tures below  the  freezing  point  of  the  dilute  solutions  in  their 
cells  and  pores.  Trees  give  off  moisture  in  winter  at  low 
temperatures  and  the  amounts  given  off  are  more  than  can 
be  explained  by  the  vaporization  of  the  ice  present  in  the 
tree  as  a  result  of  freezing,  which  indicates  that  there  must  be 
some  circulation  of  liquids,  though  this  may  be  small  in  amount. 
That  the  contents  of  the  larger  vessels  freeze  solid  is  doubtless 
true  but  whether  the  contents  of  the  very  minute  ones  freeze 
also  is  not  so  certain.  If  they  do  not,  they  could  furnish 
the  small  amount  of  circulation  which  appears  to  be  main- 
tained. When  different  specimens  of  a  single  variety  of 
tree  growing  at  different  altitudes  are  compared,  it  is  found 


1  Contribution    from    the    Chemical    Laboratory  of  the  University  of 
Michigan. 


6  Edward  A.  Rykenboer 

that  the  capillary  tubes  become  progressively  smaller  as  the 
height  at  which  the  tree  grows  is  increased.  This  seems  to 
point  to  a  natural  fortification  against  the  lower  temperatures 
experienced  at  high  altitudes.  At  any  one  altitude  the  pores 
in  the  summer  wood  are  smaller  than  those  formed  in  spring, 
but  since  the  year's  growth  is  very  small  this  would  not  neces- 
sarily indicate  that  the  smaller  tubes  were  formed  later  in 
the  season  as  a  preparation  for  winter.  We  were  unable  to 
find  any  exact  data  bearing  on  these  points,  indeed  we  did 
not  find  any  reference  to  the  considerations  just  outlined,  in 
our  examination  of  the  literature,  either  botanical,  physico- 
chemical  or  physical. 

Furthermore,  the  question  of  pore  size  as  determining, 
if  it  does  determine,  the  degrees  of  supercooling  possible  with- 
out solidification,  may  be  significant  in  connection  with  cold 
storage.  For  it  is  well  known  that  many  food  products, 
after  being  frozen  and  then  thawed,  are  less  palatable.  Possi- 
bly for  each  substance  there  is  a  temperature,  below  which  it 
should  not  be  brought. 

The  subject  seemed  to  us  of  interest  amply  sufficient 
to  justify  a  careful  study  of  the  amount  of  supercooling 
obtainable  in  capillary  tubes  and  we  hoped  we  might  possibly 
succeed  in  formulating  the  degree  of  supercooling  as  a  function 
of  the  diameter  of  the  tube. 

Discussion  of  Supercooling 

The  literature  upon  the  subject  of  supercooling  in  capil- 
lary tubes  is  very  meagre  and  is  confined  practically  to  a 
single  contribution  by  H.  C.  Sorby.1  He  made  a  brief  study 
of  the  temperatures  at  which  water  froze  in  capillary  tubes 
of  different  diameters.  He  did  this  because  he  observed  that 
in  quartz  cavities,  liquids,  that  he  supposed  to  be  water, 
remained  in  the  fluid  state  far  below  the  freezing  point  of 
water.  In  tubes  from  1/4  to  1/40  of  an  inch  in  diameter 
the  freezing  point  was  found  to  be  about  — 6°  C,  in  tubes 
smaller  than  1/40  of  an  inch  he  found  he  could  carry  the  super- 


Phil.  Mag.,  [4]  18,  105  (1859)- 


Capillary  Phenomena  and  Supercooling  7 

cooling  much  further  and  in  tubes  of  a  diameter  varying  from 
1/200  to  1/300  of  an  inch  water  froze  at  —  17°  C.  On  the 
other  hand  he  found  that  there  was  no  decided  difference  in 
the  point  at  which  freezing  occurred  in  tubes  varying  from 
1/200  to  1/700  of  an  inch  nor  in  tubes  with  diameters  from 
1/4  to  1/40  of  an  inch.  However,  while  the  values  for  the 
tubes  included  in  each  of  these  ranges  were  the  same,  the  two 
sets  of  readings  were  different.  No  conclusions  were  arrived 
at  nor  was  any  explanation  offered  for  the  phenomenon. 

Van  der  Mensbrugghe1  refers  to  supercooling  in  capillary 
tubes,  among  a  number  of  other  facts,  which  he  uses  as  ex- 
amples to  demonstrate  the  application  of  a  formula  derived 
from  thermodynamical  considerations.  The  formula  follows: 


vx 

K  =  specific  heat. 

k  =  specific  heat  if  surface  has  no  potential  energy. 

A  =  thermal  equivalent  of  the  unit  of  work. 

t  =  absolute  temperature. 

S  =  free  surface. 

T  =  potential  energy  of  surface  of  contact  (of  a  solid  and  a 

liquid  which  wets  it). 

V  —  volume. 

X  =  specific  gravity  of  the  liquid. 

The  exact  form  of  the  function  which  expresses  T  by 
means  of  t  for  any  liquid  whatever  is  not  known,  but  for  a 
given  liquid,  the  values  of  the  coefficients  of  an  equation  such 
asT  =  a  +  j8  t  -f-  7  t2  +  .  .  .  .  can  be  obtained.  According 
to  Van  der  Mensbrugghe  the  values  of  /3  and  7  for  water  are 
very  small,  and  permit  the  powers  of  t  higher  than  the  second 

d2T 
to  be  neglected.     For  the  same  liquid  -r^    is    negative    and 

from  this  it  follows  that  the  quantity  of  heat  to  be  supplied 
or  taken  away  from  unit  weight  of  water,  to  raise  or  lower  the 
temperature  one  degree,  in  general  increases  with  t  and  also 
with  S.  Consequently  it  will  be  necessary  to  supply  or  with- 
draw much  more  heat  to  raise  or  lower  the  temperature  one 

i  Phil.  Mag.,  (5)  2,  450  (1876);  (5)  4,  40  (1877). 


8  Edward  A.  Rykenboer 

degree,  if  the  total  surface  of  a  given  mass  is  increased  by  any 
means,  such  as  dividing  it  into  many  small  spheres  or  intro- 
ducing it  into  a  capillary  tube.1 

In  capillary  tubes  it  is  necessary  to  ascertain  the    sign 

d2T 

-Tfi,  m  order  to  foresee  the   quantity   of  heat  necessary  for 

a  variation  of  potential  energy  in  the  surface  of  contact  be- 
tween the  liquid  and  walls.  If  the  sign  is  negative,  we  must 
conclude  that  K  increases  with  the  surface  S  and  consequently 
the  smaller  the  tube  diameter  the  larger  will  be  the  value  of 

J2T 
K.     However,  -^  is  a  continuous  function  and  for  any  decided 

difference  in  S/V  there  ought  to  be  a  corresponding  difference 
in  K,  which  would  mean  a  difference  in  the  supercooling,  the 
other  conditions  remaining  unchanged.  A  consideration  of 
Sorby's  results  shows  that  this  is  not  the  case,  since  the  di- 
ameters vary  widely  over  ranges  of  equal  supercooling  values: 
the  value  S/V  changing  greatly  with  no  corresponding  change  in 
supercooling.  It  seemed  possible  that  Sorby's  results  were 
not  accurate  or  that  he  had  omitted  to  consider  some  important 
condition  or  source  of  error.  But  our  experiments,  described 
later,  tend  to  confirm  his  results  in  this  particular,  and  it 
becomes  evident  that  the  formula,  as  given,  is  of  doubtful 
value,  at  least  in  its  application  to  liquids  in  capillary  tubes. 
Although  supercooling  in  capillary  tubes  has  received  so 
little  attention,  the  general  subject  of  supercooling  and  the 
conditions  under  which  a  supercooled  liquid  will  crystallize 


1  The  ratio  S/V  increases  as  the  volume  of  the  mass  diminishes,  and,  con- 
sequently, since  dzT/dt2  is  negative,  the  smaller  the  diameter  of  the  mass  or 
drop  the  greater  will  be  the  value  of  K.  Van  der  Mensbrugghe  believes  that 
this  explains  how  M.  Mousson  (Bibl.  Univ.  de  Geneve,  3,  296  (1758))  was  able 
at  very  low  temperatures  to  keep  drops  of  water  of  less  than  l/z  mm  diameter 
in  the  liquid  state,  when  disposed  upon  a  surface  which  they  did  not  wet.  In 
the  same  way,  Tomlinson  (Students'  Manual  of  Natural  Philosophy,  p.  553) 
could  see  minute  drops  of  water,  alcohol  and  ether  roll  upon  the  surface  of  a 
fixed  oil  raised  to  more  than  200°  C. 

In  this  connection  it  can  be  shown  that  the  sign  d2T/dtz  changes  under 
certain  conditions:  for  water  the  change  occurs  in  the  vicinity  of  the  maximum 
density. 


Capillary  Phenomena  and  Supercooling  9 

spontaneously  has  been  the  subject  of  a  good  deal  of  study. 
Summarizing  the  results  we  may  say  that  the  spontaneous 
crystallization  of  a  supercooled  liquid  depends  upon  two 
factors : 

(a)  On  the  spontaneous  power  of  crystallization:  this  is 
determined,  and  can  be  measured,  by  the  number  of  centers 
of  crystallization  which  are  formed  per  unit  of  time  in  unit 
mass  of  the  liquid. 

(b)  On  the  velocity  with  which  the  boundary  between 
liquid  and  crystal  is  shifted  (i.  e.,  velocity  of  crystallization). 

Crystallization1  in*  a  supercooled  liquid  never  occurs 
homogeneously  throughout  the  whole  mass  of  the  liquid  but 
always  begins  at  certain  points  or  centers  of  crystallization, 
the  number  of  which  depends  upon  the  amount  and  duration 
of  the  supercooling  and  the  volume  of  the  supercooled  mass. 
Crystal  threads  grow  outwards  from  these  centers  and  spherical 
crystal  aggregates  result.  In  many  substances  the  number 
of  centers  can  be  determined  by  counting  the  spherical  crystals, 
each  crystal  aggregate  containing  a  center  of  crystallization. 
For  this  purpose  the  material,  enclosed  in  a  thin-walled  glass 
tube,  is  heated  just  above  the  melting  point  and  is  then  rapidly 
cooled  40°  to  80°.  Then  the  centers  usually  begin  to  appear. 
If  they  appear  too  slowly  the  tube  can  be  warmed  slightly 
and  the  number  of  centers  will  be  increased,  but  the  velocity 
of  crystallization  increases  also,  so  that  the  whole  mass  tends 
to  crystallize  when  the  first  center  appears  and  the  counting 
is  soon  ended.  With  increasing  initial  supercooling  the 
number  of  centers  formed  per  time  and  temperature  unit 
increase  at  first  to  a  maximum,  but  at  temperatures  about 
100°  below  the  melting  point  the  number  formed  per  unit 
time  decreases  rapidly.  This  behavior  is  well  shown  in  the 
case  of  piperin  as  is  manifest  in  the  two  tables  following:2 
The  amount  of  substance  used  in  each  case  was  1/8  cc. 
The  melting  point  of  piperin  is  129°  C. 


1  Tamman:  Zeit.  phys.  Chem.,  25,  443  (1898). 

2  Tammann:  Loc.  cit. 


10 


Edward  A.  Rykenboer 
TABLE  I 


Cooled  quickly 
to/°C 

Time 
Minutes 

No.  of  centers 

35-1 

2 

o 

4 

2 

8 

3 

12 

5 

40.2 

2 

4 

4 

10 

8 

19 

12 

23 

45.  i 

2 

i 

4 

3 

8 

5 

12 

7 

TABLE  II 


No.  of  centers 


25.2 

38 

32 

30.1 

73 

62 

35-2 

IO2 

96 

40.  i 

132 

141 

45-2 

I  O6 

in 

50.2 

92 

96 

55-3 

85 

88 

60.  i 

52 

43 

65-2 

27 

24 

70.2 

8 

7 

75  •  I 

o 

i 

In  Table  II  the  number  of  centers  given  is  in  every  case 
the  number  which  appeared  in  exactly  two  minutes. 

Table  III  shows  the  relation  between  the  volume  of  the 
liquid  and  the  number  of  crystal  nuclei. 

TABLE  III 


/ 

Cylinder  I 

Cylinder  II 

Cylinder  III 

0.25  cc 

0.5  cc 

1.2  CC 

0 

i 

I 

18 

20 

4 

5 

58 

40 

39 

50 

148 

60 

6 

8 

76 

Capillary  Phenomena  and  Supercooling 
TABUS  III— (Continued') 


ii 


Cylinder 

Lg.  cm 

Outer  diam. 
cm 

Thickness  of 
wall  cm 

Volume 
cc 

I 
II 
III 

26.0 
23.0 
4.2 

0.  II 

0.18 
0-53 

O.O2 
0.02 

0.04 

0.25 
0.50 

1.20 

Figure  I  shows  the  graphical  representation  of  the  values 
given  in  Table  III.1 

The  most  significant  facts  brought  out  by  this  figure  are 
that  the  number  of  crystal  nuclei  is  not  proportional  to  the 

volume  of  the  containing  cyl- 
inder and  that  the  maximum 
value  for  each  curve  comes  at 
the  same  point  on  the  tem- 
perature axis.  In  general, 
however,  the  number  of  centers 
is  greater,  the  greater  the  vol- 
ume of  the  liquid,  as  would 
naturally  be  expected. 

The  second  determining 
factor  in  the  spontaneous  crys- 
tallization of  a  supercooled 
liquid  is  the  velocity  of  crys- 
tallization, or  the  speed  with 
which  the  boundary  between 
liquid  and  crystal  is  shifted.  If  the  velocity  is  very  small,  centers 
might  appear  but  they  could  not  grow  and  the  liquid  would  not 
crystallize.  Piperin,  for  example,  can  be  melted,  then  cooled 
until  several  centers  appear  and  then  if  the  temperature  is 
lowered  rapidly  the  centers  remain  the  same  size,  and  will 
not  change  until  the  temperature  is  again  increased  to  a 
region  where  the  velocity  of  cystallization  is  noticeable.  To 
determine  the  velocity,  the  molten  liquid  is  supercooled  in 
a  U-tube  and  inoculated  at  one  end  with  a  crystal  nucleus. 
As  time  passes  the  crystal  surface  can  be  seen  to  grow.  If 

1  Tammann:  Loc.  cit. 


Fig.  I 


12 


Edward  A.  Rykenboer 


crystallization  velocity  is  plotted  against  temperature  a  dia- 
gram will  be  obtained  similar  to  Figure  II.1 


S 


M.P 


aascanainy 

Fig.  II 


In  considering  this  diagram  three  things  must  be  borne 
in  mind:  (i)  Bath  temperatures  are  represented  on  the 
horizontal  axis.  (2)  The  temperature  at  the  boundary  layer 
between  crystal  and  liquid  is  not  the  temperature  of  the  bath, 
on  account  of  the  heat  of  crystallization.  (3)  When  layers 
of  liquid  relatively  far  from  the  boundary  layer  are  heated 
to  the  melting  point,  due  to  heat  of  crystallization,  the  velocity 
is  high.  If  a  thin  layer  only  is  heated  to  the  melting  point, 
the  velocity  will  have  a  constant  value  as  long  as  the  heat 
of  crystallization  is  sufficient  to  maintain  this  temperature  in 
a  thin  layer.  As  the  temperature  at  the  boundary  falls  the 
velocity  decreases  still  further. 

At  first,  in  range  A,  as  the  temperature  of  the  bath  is 
lowered,  the  values  for  velocity  are  small.  The  reason  for 
this  is  that,  owing  to  the  insufficiently  rapid  removal  of  heat 
or  crystallization,  layers  of  liquid  adjacent  to  the  crystallizing 
boundary  are  heated  to  temperatures  even  above  the  melt- 
ing point  and  the  penetration  of  the  crystal  nuclei  into  these 
layers  is  retarded.  In  range  B  the  velocity  increases,  in  spite 
of  the  fact  that  the  bath  temperature  is  lower,  since  the  heat  of 
crystallization  is  sufficient  to  cause  layers,  that  are  far  from 
the  crystallizing  layer,  to  be  heated  to  the  melting  point. 
As  the  temperature  of  the  bath  decreases  still  further  in  range 
C,  only  enough  heat  is  furnished  to  establish  the  melting 


1  Tammann:  Zeit.  Elektrochemie,  10,  532  (1904). 


Capillary  Phenomena  and  Supercooling 


point  temperature  in  a  thin  layer.  If  the  maximum  velocity 
is  less  than  3  mm  per  minute,  the  heat  liberated  per  unit  of  time 
is  usually  not  sufficient  to  maintain  the  temperature  of  the 
melting  point  constantly  at  the  boundary  for  an  extended  fall 
of  temperature  in  the  bath,  and,  in  consequence,  range  C 
shrinks  to  a  point.  Furthermore,  with  substances  showing  a 
rather  high  velocity  the  heat  liberated  will  heat  layers  of 
liquid,  still  farther  from  the  crystallizing  boundary,  as  in 
range  B,  and  the  curve  will  continue  to  rise  beyond  C  into 
range  D.  In  this  range  the  velocity  will  rise  to  its  maximum 
value.  Finally,  in  range  E  the  heat  of  crystallization  is  no 
longer  sufficient  to  establish  the  melting  point  temperature 
even  in  a  thin  layer,  and  the  velocity  decreases  with  increasing 
supercooling. 

The  viscosity  is  also  related  to  the  spontaneous  power 
of  crystallization  and  to  the  velocity,  and  its  relation  is  brought 
out  by  the  curves  in  Figure  III.1 


power 
III  -  velocity 


Fig.  Ill 

The  viscosity  of  the  liquid  increases  with  descending 
temperature  and  frequently,  in  a  small  range  of  temperature, 
passes  thiough  all  values  from  those  of  a  syrupy  liquid  to 
those  of  a  solid  mass,  and  if  the  temperature  is  still  further 
lowered  the  mass  becomes  hard  and  brittle.  After  passing 
the  temperature  range  in  which  the  maximum  number  of 
centers  of  crystallization  are  formed,  the  viscosity  becomes 
very  large  and  few,  if  any,  centers  appear  in  the  brittle,  glassy 

1  Tammann :  Loc.  cit. 


14  Edward  A.  Rykenboer 

mass.  If  centers  did  form  they  would  not  grow  on  account  of 
the  very  small  values  of  crystallization  velocity  in  this  region 
and  the  substance  becomes  highly  stable,  since  the  number 
of  centers  of  crystallization  is  a  measure  of  the  instability  of 
a  supercooled  liquid.  The  more  there  are,  the  greater  is  the 
tendency  of  the  liquid  to  change  its  state  of  aggregation.  A 
liquid  can  therefore  be  the  more  easily  undercooled  the  fewer  the 
nuclei  in  it,  and  the  more  slowly  these  nuclei  grow. 

Subject  of  Investigation 

We  undertook  to  ascertain  experimentally  the  maximum 
degrees  of  supercooling  obtainable  in  glass  tubes  with  diameters 
varying  from  about  one-half  a  centimeter  down  to  the  small- 
est we  could  conveniently  manipulate.  Our  purpose  was  to 
settle  the  question  as  to  whether  supercooling  could  be  more 
easily  produced  and  could  be  carried  further  in  capillary 
tubes  than  in  larger  tubes.  Our  hope  was  to  find  and  estab- 
lish some  mathematical  relation  between  the  maximum  super- 
cooling effect  and  the  diameter  of  the  tube.  And  our  intention 
was  to  include  a  number  of  different  substances  in  the  in- 
vestigation. 

At  first  the  experiments  were  confined  to  a  study  of 
water  as  the  supercooled  liquid.  Mixtures  of  ice  and  salt 
were  employed  as  cooling  agents,  but  they  proved  to  be  a 
source  of  annoyance  duetto  the  fact  that  the  apparatus  soon 
became  encrusted  with  a  layer  of  salt,  which  made  it  practically 
impossible  to  take  readings  on  the  thermometer  immersed 
with  the  supercooled  tubes.  Solutions  of  solid  carbon  dioxide 
in  ether  or  in  alcohol  were  also  used,  as  was  a  current  of  carbon 
dioxide  gas  escaping  from  a  pressure  tank  and  therefore  cold, 
due  to  the  expansion.  The  solutions,  of  course,  evaporated 
rapidly  and  it  became  evident  that  the  quantities  we  should 
have  to  use  would  involve  too  great  a  cost.  We  therefore 
abandoned,  for  the  time  at  least,  our  originally  planned  work 
on  water,  and  solutions  in  water,  and  turned  our  attention  to 
materials  whose  melting  points  were  between  100°  and  125°. 
With  these,  all  the  cooling  that  was  needed  was  obtained  by 


Capillary  Phenomena  and  Supercooling  15 

allowing  the  temperature  of  the  bath  containing  the  experi- 
mental tubes  to  fall  gradually  to  that  of  the  room.  Almost 
all  of  the  work  was  done  with  sulphur,  oxalic  acid,  orthoacet- 
toluid,  /3-naphthol  and  acetanilide.  These  substances  were 
chosen  because,  with  the  exception  of  oxalic  acid,  they  do 
not  decompose  at  temperatures  near  their  melting  points. 

Method  and  Apparatus 

The  material,  enclosed  in  glass  tubes  immersed  in  a  bath, 
was  first  heated  to  a  temperature  a  few  degrees  above  its 
melting  point.  It  was  held  at  this  point  until  all  had  melted ; 
the  temperature  was  then  allowed  to  fall  and  the  temperature 
at  which  crystallization  began  in  each  tube  was  noted. 

Along  with  each  series  of  capillary  tubes  was  included 
one  large  or  standard  tube.  This  tube  was  of  sufficient  di- 
ameter so  that  the  enclosed  mass  represented  a  volume  so 
large  that  the  number  of  nuclei  formed  was  considerable  and 
the  tube  gave  the  smallest  possible  values  for  supercooling. 
This  condition  was  fulfilled  by  tubes  having  diameters  from 
4  to  5  mm,  which  was  smaller  than  we  had  anticipated. 
Numerous  larger  tubes  were  tried  but  none  of  them  gave 
supercooling  values  different  from  those  obtained  with  the 
4  to  5  mm  tubes.  We  then  fixed,  as  it  were,  the  upper  limit 
above  which  the  effects  we  were  studying  were  not  to  be  ex- 
pected. Tubes  of  this  dimension  we  called  our  standard  or 
comparison  tubes. 

Ordinary  soft  glass  tubing  was  steamed  well  to  get  rid  of 
any  soluble  material  and  then  left  standing  for  several  hours 
filled  with  the  usual  potassium  bichromate-sulphuric  acid 
cleaning  mixture.  It  was  then  washed  with  distilled  water, 
dried  by  drawing  through  it  a  current  of  air,  and  drawn  down 
to  the  capillary  sizes  desired  in  the  blast  lamp.  Suitable 
lengths  of  the  capillary  were  then  cut  off  with  a  small  flame, 
thus  sealing  both  ends.  These  little  tubes  were  left  sealed 
until  we  were  ready  to  fill  a  series  and  start  a  set  of  observations. 
In  filling  the  tubes  the  substance  to  be  used  was  heated  just 
above  its  melting  point  and  held  there  until  the  whole  mass 


1 6  Edward  A.  Rykenboer 

had  melted.  The  tubes  selected  were  opened,  warmed  and 
their  ends  were  dipped  into  the  liquid  where  they  filled  by 
capillary  ascension.  They  were  then  removed  and  the  sub- 
stance, still  liquid,  was  drawn  up  by  suction  into  the  tube  far 
enough  to  allow  the  end  to  be  sealed.  The  tubes  were  then 
reheated  to  a  few  degrees  above  the  melting  point  of  the  sub- 
stance in  a  bath  and  any  leak  could  be  detected  by  the  as- 
cension of  bath  liquid  in  that  tube.  Ordinarily,  the  length 
of  the  column  of  substance  was  only  a  few  millimeters. 

In  order  to  regulate  the  rate  of  cooling,  and  in  order  to 
have  normally  a  rather  slow  rate  of  cooling,  it  was  found 
necessary  to  use  a  bath  of  from  600  cc  to  800  cc  capacity. 
A  large  beaker  answered  our  purpose  and  an  inner  bath  served 
to  keep  the  temperature  more  nearly  uniform  for  all  the  tubes 
contained  within  it.  A  variety  of  different  liquids  were  tried 
in  the  bath  but  sulphuric  acid  was  finally  chosen  in  spite  of 
certain  risks  of  accidents  thus  entailed.  The  great  advantage 
of  sulphuric  acid  was  that  it  could  be  used  over  a  large  range 
of  temperature,  but  after  repeated  heatings,  it  was  found  that 
it  was  satisfactory  only  for  temperatures  below  225  degrees. 
The  bath  was  placed  upon  sand  and  an  ordinary  Bunsen 
burner  was  used  for  the  heating. 

After  experimenting  with  several  methods  of  stirring,  a 
device  was  finally  adopted  which  consisted  of  an  inner  bath 
of  glass,  a  tube  3  cm  in  diameter  and  22  cm  long,  closed  at 
the  lower  end.  The  upper  end  projected  through  the  center 
of  a  horizontal  wooden  wheel  to  which  it  was  firmly  attached. 
This  wheel  was  supported  on  ball  bearings  and  was  rotated 
by  an  electric  motor.  Projecting  almost  to  the  bottom  of  the 
inner  bath  was  a  small  glass  tube  which  had  attached  to  it, 
two  platinum  carriages.  The  capillary  tubes,  usually  three 
or  four  in  number,  projected  through  openings  in  these  car- 
riages and  were  fastened  at  the  top  to  the  glass  tube  by  means 
of  an  ordinary  rubber  band.  The  glass  tube  was  fastened  to 
a  separate  support  and  being  stationary,  while  the  inner  bath 
was  rotated,  the  arrangement  effected  the  stirring. 

A  thermometer  extended  through  the  glass  tube  and  its 


Capillary  Phenomena  and  Supercooling 


mercury  bulb  was  at  the  same  level  in  the  bath  as  the  material 
enclosed  in  the  capillary  and  standard  tubes.  The  thermometers, 
ten  inches  long,  were  made  especially  for  this  work  and  have 
a  scale  about  five  inches  in  length  on  the  lower  half,  while 
the  upper  half  is  left  blank  for  purposes  of  fastening  in  position. 
In  this  way  the  whole  scale  was  immersed  in  the  liquid  of  the 
bath  and  no  correction  was  necessary.  While  this  was  not 


-Su&por/  /or  inner 
(Bafl  baar/n?   c*rrt 


Platinum   carriage 
Oufar  bafh 


--Platinum  carriage 
-  Thormomcfar 


Fig.  IV 

important,  the  readings  were  much  more  easily  followed  where 
the  whole  scale  was  visible.  The  scales  were  made  in  seventy- 
five  degree  lengths  and  each  succeeding  thermometer  over- 
lapped the  one  before  by  twenty-five  degrees.  The  ther- 
mometer, being  removable,  permitted  the  use  of  a  wide  range 
in  temperature  because  one  thermometer  could  be  taken  out 
and  another  covering  a  different  range  could  be  inserted. 


1 8  Edward  A.  Rykenboer 

The  arrangement  of  tubes  and  thermometer  is  shown  in 
Figure  IV. 

It  was  necessary  to  have  an  adjustable  means  for  regu- 
lating the  rate  of  cooling  of  the  outside  bath.  A  cooling  coil 
of  water  was  out  of  the  question,  since  the  cold  coil,  immersed 
in  the  acid  at  perhaps  two  hundred  degrees,  might  break 
and  under  these  conditions,  explosions  and  serious  accidents 
might  result.  A  cooling  coil  of  sulphuric  acid  was  tried  but 
was  not  found  to  be  very  efficient  unless  of  a  size  so  large  that 
it  would  interfere  with  the  readings.  Finally  a  satisfactory 
method  was  devised  -by  means  of  which  cold  sulphuric  acid 
was  added  while  the  hot  acid  was  simultaneously  drawn  off, 
thus  keeping  the  bath  at  a  constant  level.  By  means  of  a 
suction  flask  and  pump  connected  with  a  two-liter  bottle, 
the  hot  acid  was  drawn  through  a  glass  tube  at  the  top  of  the 
bath,  passed  through  condensers  for  the  purpose  of  cooling 
it  and  then  was  allowed  to  fall  into  a  bottle.  At  the  same  time, 
by  means  of  a  pressure  flask,  cold  acid  was  forced  into  the 
bath  from  a  reservoir  immersed  in  running  water.  For  most 
substances  this  cooling  was  sufficient,  but  in  cases  where  the 
substance  had  a  low  melting  point  it  was  necessary  to  keep 
the  reservoir  surrounded  with  a  mixture  of  salt  and  ice.  These 
two  outfits  were  so  connected  that  by  turning  several  valves 
the  cooled  acid  was  drawn  over  into  the  reservoir  and  the 
process  was  ready  to  be  repeated.  Though  the  apparatus 
looked,  and  was,  rather  complicated  it  was  very  quickly  and 
easily  set  in  action  or  stopped.  Figure  V  shows  the  arrange- 
ment. 

In  carrying  out  the  experimental  part  of  the  work  it  was 
necessary  first,  to  select  a  thermometer  such  that  the  melting 
point  of  the  material  enclosed  in  the  tubes  came  near  the  top 
of  its  scale.  Then  supercooling  values  could  be  read  on  the 
same  thermometer.  In  some  cases  the  supercooling  was  so 
great  that,  in  spite  of  this  precaution,  another  thermometer 
covering  a  lower  range  had  to  be  substituted  later.  The 
thermometer  and  tubes  were  adjusted  as  previously  described 
and  the  temperature  was  gradually  raised  to  a  point  not  more 


Capillary  Phenomena  and  Supercooling 


Fig.  V 

To  Cool  Bath:  Open  cock  i,  close  9  and  turn  the  three-way  cock  3, 
closing  it  to  5  and  leaving  it  open  from  2  to  4.  Then  the  suction  of  the  water 
pump  draws  the  acid  from  the  bath  F  through  the  condensers  into  the  cooling 
bottle  A.  At  the  same  time  leave  cocks  6  and  7  open  with  8  closed  and  water 
from  reservoir  E  flows  into  pressure  bottle  C  and  causes  the  acid  in  D  to  pass 
through  cock  6  into  the  bath. 

To  bring  apparatus  back  to  the  original  conditions:  Close  i,  turn  cock  3 
so  that  4  is  open  to  5,  close  cock  6,  open  9,  open  7  leaving  8  closed  and  suction 
draws  the  acid  back  into  D  and  at  the  same  time  draws  the  water  from  C  into  E. 
Cock  8  is  to  relieve  the  partial  vacuum  in  C  after  the  process  is  completed. 


2o  Edward  A.  Rykenboer 

than  five  degrees  above  the  melting  point  of  the  substance 
under  investigation.  With  rapid  heating  the  temperature  of 
the  inner  bath  lagged  behind  that  of  the  outer  bath,  so,  as  the 
temperature  of  the  outer  bath  approached  the  melting  point,  the 
rate  of  heating  was  gradually  decreased.  In  this  way  it  was 
possible  to  keep  the  temperature  of  heating  from  going  more 
than  five  degrees  above  the  melting  point.  The  heating  burner 
was  then  removed  and  the  bath  allowed  to  stand  until  the 
temperature  had  dropped  several  degrees.  The  cooling 
arrangement  was  then  used  to  bring  the  batty  down  almost 
to  the  temperature  which  had  been  found  by  previous  experi- 
ments to  be  the  point  where  the  material  in  the  standard  tube 
solidified.  The  bath  was  then  allowed  to  cool  more  slowly, 
subject  only  to  the  cooler  temperature  of  the  room.  A  four- 
inch  reading  glass  was  used  to  magnify  the  smaller  tubes  so 
that  the  formation  of  the  first  nucleus  could  be  noticed  more 
readily.  Immediately  that  this  was  seen,  the  temperature 
was  read  from  the  thermometer  within  the  inner  bath.  The 
liquid  of  the  bath  also  magnified  the  tubes  within  so  there 
was  no  difficulty  in  making  the  required  observation  even 
with  the  smallest  capillaries  used.  There  was  also  no  diffi- 
culty in  noting  when  solidification  began,  since  the  transparent 
contents  of  a  tube  immediately  became  opaque,  due  to  the 
solidified  material  enclosed.  This  procedure  was  repeated 
several  times  for  each  set  of  tubes  and  successive  values  of 
supercooling  were  obtained.  After  such  a  series  of  readings 
had  been  obtained  the  tubes  were  removed  from  the  bath. 
The  length  of  the  column  of  confined  material  was  then  mea- 
sured to  tenths  of  a  millimeter  and  the  diameter  in  millimeters 
to  three  decimal  places.  The  diameter  was  obtained  by  break- 
ing the  tube  at  a  point  where  the  material  was  enclosed  and 
then  inserting  a  short  section  of  the  tube  vertically  in  a  small 
clamp  attached  to  a  metal  object  plate.  This  plate  was  then 
put  on  the  stage  of  a  microscope  and  the  inner  diameter  of 
the  tube  was  measured  by  means  of  a  calibrated  scale  in  the 
ocular.  A  micrometer  attachment  allowed  a  hair  to  be  moved 
across  the  field  from  one  side  of  the  tube  to  the  other,  the 


Capillary  Phenomena  and  Supercooling 


21 


movement  being  read  directly  by  means  of  a  calibrated  drum 
on  the  ocular.  The  number  of  divisions  on  the  drum  multi- 
plied by  their  actual  value  for  the  objective  used  gave  the 
results  in  millimeters.  Several  readings  were  taken,  as  the 
cross  sections  of  the  tubes  were  not  perfectly  circular,  and 
the  mean  value  was  recorded. 

Results 

The  tables  following  give  results  obtained  with  some  of 
the  materials  used.  The  data  for  all  of  our  materials  are  not 
given,  nor  are  all  the  data  for  a  single  substance  shown.  It 
is  unnecessary  to  give  'more  than  we  have  given,  since  all 
results  obtained  were  similar  to  those  recorded.  By  degrees 
of  supercooling  is  meant  the  temperature  at  which  the  first 
crystallization  was  observed,  counting  downward  from  the 
melting  point  of  the  substance.  For  instance,  with  sulphur, 
crystallization  was  first  noted  in  tube  41  at  92°  C.  Then 
114  —  92  =  22  degrees  of  supercooling. 

The  tubes  are  arranged  in  the  tables  in  the  order  of 
creasing  mean  diameter.     In  all  tables  L,g.  Col.  =  Lenj 

TABU*  IV 
Sulphur  M.  P.  =  114-115°  C 


Tube 
No. 

Mean 
Diam. 
in  mm 

Lg.  Col. 
in  mm 

S.  C.  i 

S.  C.  2 

S.  C.3 

S.  C.  4 

S.C.5 

S.  C.  6 

30 

0.164 

7.0 

49.0 

49-5 

56-5 

59.1 

— 

— 

29 

0.187 

5-5 

44-5 

5i-5 

44.4 

57-o 

56.5 

56.0 

25 

0.227 

5-6 

52.2 

62.5 

62.2 

62.0 

61.7 

61.6 

32 

0.233 

ii.  5 

55-5 

58.8 

58.5 

52.4 

61.6 

54-4 

28 

0.260 

4-5 

41  .0 

60.4 

55-6 

56.2 

56.7 

58-2 

31 

0.312 

4.2 

53-8 

54«5 

65-5 

57-6 

61.2 

66.5 

44 

0.318 

5-4 

43-0 

43-8 

44.2 

47-3 

44-7 

42.7 

35 

0.319 

5-7 

48.8 

57-2 

57-o 

5i-5 

63-2 

60.2 

26 

0.389 

5-5 

46-3 

52.0 

55-5 

64.8 

60.5 

60.0 

24 

0.402 

7.0 

53-5 

5^.2 

42.2 

— 

— 

— 

27 

0-434 

6.5 

43-2 

47-3 

39-2 

40.2 

50.5 

39-7 

45 

0-544 

6.4 

38.2 

38.0 

42.0 

45-5 

41.0 

40.8 

61 

4.1 

4-5 

30.4 

31.0 

27-5 

28.5 

30.0 

— 

4i 

4-5 

3-5 

22  .O 

20.8 

26.5 

24.2 

24.8 

27.0 

22 


Edward  A.  Rykenboer 


Column  of  material  enclosed  in  tube;  Mean  Diam.  =  Mean 
Diameter  of  tubes;  S.  C.  =  Degrees  of  Supercooling;  S.  C.  i, 
S.  C.  2,  etc.,  represent  values  for  successive  heatings  and  cool- 
ings. Table  IV  contains  some  of  the  results  obtained  with 
sulphur. 

TABLE  V 
Orthoacettoluid.     M.  P.  =  110°  C 


Tube 
No. 

Mean 
Diam. 
in  mm 

Ivg.  Col. 

in  mm 

S.  C.  i 

S.  C.   2 

S.  C.  3 

S.  C.  4 

S.  C.  5 

S.  C.6 

69 

0.209 

5-0 

37-0 

34-8 

36.4 

35-o 

36.0 

39-6 

77 

0.223 

— 

38.7 

35-5 

— 

— 

— 

— 

68 

0.291 

4-4 

29.2 

29.8 

3i-5 

33-1 

33-5 

32.2 

67 

0.401 

5-i 

30.5 

30.5 

30-9 

32.9 

33-0 

32.9 

72 

0.471 

— 

29-5 

33-9 

29.9 

33-5 

33-6 

— 

66 

0.530 

3-2 

29-3 

30.8 

31.0 

32.0 

33-8 

33-5 

65 

0.568 

5-i 

31-6 

32.1 

33-7 

35-7 

34-8 

35-4 

7i 

0.727 

— 

34-5 

3i-7 

31.2 

33-5 

34-9 

— 

64 

4.0 

4-5 

23.0 

23-5 

22.5 

24.2 

24.2 

25.0 

70 

4-o 

— 

19.6 

23-8 

24.0 

18.6 

24.2 

— 

64  and  70  were  the  standard  tubes. 

TABLE)  VI 
0-Naphthol.     M.  P.  =  122°  C 


Tube 
No. 

Mean 
Diam. 
in  mm 

Lg.  Col. 
in  mm 

S.  C.  i 

S.  C.   2 

S.  C.  3 

S.  C.  4 

S.  C.5 

S.  C.6 

80 

0.327 

4-2 

16.8 

18.0 

17.0 

16.6 

17.8 

19.2 

91 

0.342 

5-i 

ii.  8 

13-3 

16.2 

13.2 

— 

— 

83 

0-353 

4.0 

14.7 

16.0 

14.1 

17-5 

18.2 

17.4 

79 

0.382 

4.0 

14-5 

15.0 

16.7 

16.7 

18.5 

16.0 

82 

0-394 

5-0 

10.5 

16.4 

13.0 

16.3 

18.6 

17-3 

90 

0.409 

9-5 

14.0 

13-2 

16.0 

16.0 

— 

— 

81 

0.420 

II.  0 

13.0 

13-0 

14-5 

16.2 

16.2 

16.3 

89 

0-459 

5-2 

15-8 

15-7 

18.3 

16.7 

— 

— 

88 

0.499 

4.1 

15.7 

15.6 

16.1 

16.3 

•     — 

— 

87 

0.672 

2.5 

14.7 

14.0 

15-5 

16.8 

—  - 

— 

86 

0.695 

3-2 

15-3 

i8'.4 

17-5 

17-5 

— 

— 

85 

4-3 

4.1 

6.5 

5-6 

5-4 

6.0 

— 

— 

84 

4-3 

4.0 

5-5 

4-5 

4-5 

4-5 

5-2 

5-5 

84  and  85  were  the  standard  tubes. 

Capillary  Phenomena  and  Supercooling  23 

41  and  6>i  were  the  standard  tubes  and  it  can  be  seen  that 
the  supercooling  was  much  less  than  with  the  capillary  tubes. 
35  and  44  were  practically  the  same  in  size  and  yet  there  was 
a  decided  difference  in  the  results.  In  this  short  table  it 
looks  as  though  27  and  45,  the  largest  of  the  capillary  tubes, 
gave  supercoolings  that  were  consistently  less  than  those  of 
the  smaller  tubes,  but  these  were  exceptional  cases,  and  later 
it  will  be  seen  that  very  small  tubes  give  supercoolings  no 
greater  than  those  given  by  tubes  of  this  size  or  even  larger. 

Table  IV  shows  that  it  was  impossible  to  obtain  the 
same  results  in  successive  observations.  This  is  equally  true 

TABUS  VII 
Acetanilide.     M.  P.  =  114°  C 


Tube 
No. 

Mean 
Diam. 
in  mm 

Lg.  Col. 
in  mm 

S.  C.  i 

S.  C.  2 

S.  C.  3 

S.C.4 

S.  C.5 

S.  C.  6 

131 

0.174 

5-6 

46.6 

47-8 

42.5 

47-3 

— 

— 

123 

0.182 

5-5 

48.0 

48.0 

— 

— 

— 

— 

129 

0.189 

6-5 

47.6 

46.7 

47.2 

47.0 

— 

— 

130 

0.203 

4-5 

47-7 

46.7 

46.8 

47-4 

— 

— 

126 

0.206 

7.2 

47-7 

47-4 

46.6 

45-6 

— 

— 

128 

0.213 

5-4 

45-3 

47-5 

46.8 

46.9 

— 

— 

132 

0.234 

4-4 

46.6 

40.5 

43-6 

44.6 

— 

— 

127 

0.248 

4-5 

45-2 

46.5 

45-8 

45-3 

— 

— 

I2O 

0.249 

2.4 

47.0 

47-7 

— 

— 

— 

— 

121 

0.249 

5-8 

47.6 

43-7 

— 

— 

— 

— 

122 

0.264 

4-3 

46.9 

46.0 

— 

— 

— 

— 

125 

0.285 

1.8 

47-6 

47-5 

46.5 

45-2 

— 

— 

117 

0.328 

5-i 

46.0 

45-4 

— 

— 

— 

— 

114 

0-433 

3-3 

42.9 

45-3 

45-i 

45-6 

44-7 

— 

118 

0.336 

3-2 

46.8 

47.6 

— 

— 

— 

— 

119 

0.336 

4.0 

45-o 

46.0 

— 

— 

— 

'  — 

116 

0-353 

4-5 

46.  i 

45-5 

— 

— 

— 

— 

U3 

0.405 

3-i 

44-7 

46.0 

45-o 

45-0 

46.0 

— 

112 

0.409 

4.0 

44-o 

45-2 

43-9 

44.1 

44.6 

— 

1  10 

0.466 

2.5 

43-8 

45-3 

45-1 

44-7 

46.0 

— 

108 

0.575 

5-i 

43-i 

43-i 

43-6 

44.2 

44.0 

— 

III 

0.677 

1.8 

— 

43-0 

41  .0 

41.9 

43-4 

— 

109 

0.698 

4-5 

38.7 

38.7 

39-8 

42.0 

38.8 

— 

115 

4-3 

5-o 

37-5 

37-5 

— 

— 

— 

— 

124 

4.8 

6.5 

36.7 

33-0 

36.4 

38.4 

— 

— 

115  and  124  were  the  standard  tubes. 

Edward  A.  Rykenboer 


for  the  tables  to  follow.  In  some  cases  differences  were  very 
slight,  but  in  many  instances  they  were  large.  It  is  notori- 
ously difficult  to  get  concordant  results  upon  supercooling, 
and  bearing  this  in  mind,  it  may  be  conceded,  at  least  by  those 
who  have  ever  tried  such  experiments,  that  the  results  check 
better  than  might  have  been  expected. 

Here,  although  there  was  a  wide  range  of  tube  diameter, 
the  readings  were  almost  the  same  in  value.  The  smallest 
tubes  gave,  in  some  cases,  equal  supercooling  or  even  smaller 
supercooling  than  the  largest  tubes,  and  we  naturally  expect 
them  to  give  uniformly  higher  values  in  all  cases.  Here,  also, 
a  capillary  tube  109  gave  the  same  reading  as  the  standard 
tube  124. 

TABLE)  VIII 
Oxalic  Acid.     M.  P.  =  98°  C 


Tube 
No. 

Mean 
Diam. 
in  mm 

Lg.  Col. 

in  mm 

S.  C.  i 

S.  C.  2 

S.  C.  3 

145 

0.  191 

— 

17-5 

19.0 

17-5 

148 

0.  192 

— 

19-5 

23-5 

17.0 

150 

0.195 

— 

16.0 

15-3 

22.2 

147 

0.210 

— 

19.4 

15.0 

21-5 

149 

0.219 

— 

15-5 

16.5 

20.5 

IOI 

0.238 

i-5 

19.4 

24.1 



146 

0.242 

— 

15.0 

14-5 

15.0 

151 

0.253 

— 

10.5 

10.8 

I6.5 

100 

0.278 

1.6 

15-9 

— 



143 

0-339 

4.0 

— 

17.0 

17.0 

96 

0.352 

2.6 

15.5 

9.2 



97 

0.376 

i  .  i 

16.6 

II  .2 



155 

0.461 

6.0 

9.6 

9-0 

IO.O 

98 

0-475 

3-4 

12.5 

13.0 



99 

0.508 

i-7 

20.3 

17.6 



156 

0.585 

8-5 

7.0 

II.  O 

8.0 

95 

0.589 

4-4 

14.0 

II  .0 

— 

154 

0-739 

6.6 

3-5 

3.6 

16.0 

94 

0-755 

4-5 

16.0 

12.9 

— 

142 

4.1 

8.0 

3-5 

3-5 

7-5 

93 

4.2 

4.8 

5-5 

8.0 

— 

93  and  142  were  the  standard  tubes. 


Capillary  Phenomena  and  Supercooling  25 

Where  the  length  of  the  column  is  not  given  it  is  because 
the  thread  of  substance  itself  was  broken  into  small  segments 
due  to  the  repeated  heating.  A  column  of  from  4  mm  to  6  mm 
in  length  sometimes  broke  up  into  as  many  as  a  dozen  parts. 
This  might  have  been  caused  by  a  slight  decomposition  of 
the  acid  as  this  splitting  up  was  most  pronounced  with  oxalic 
acid  which  loses  its  water  of  hydration  just  above  its  melting 
point.  The  substance  was  heated  to  only  a  few  degrees  above 
its  melting  point,  just  enough  to  make  sure  that  all  the  ma- 
terial had  melted.  Sometimes  the  different  fragments  solidi- 
fied at  different  temperatures,  but  usually  they  all  crystallized 
out  at  the  same  time.  ' 

Here,  again,  some  of  the  larger  capillaries  gave  S.  C. 
values  almost  as  small  as  those  found  in  the  standard  tubes 
93  and  142 .  In  tubes  145  to  15 1  columns  of  acid  crystallized  out 
at  different  temperatures,  and  on  reheating  these  columns 
broke  into  a  number  of  smaller  segments,  yet  the  results  do 
not  indicate  that  this  further  subdivision  had  much  if  any 
effect  on  the  amount  of  supercooling.  In  some  cases  the  read- 
ings were  even  higher  than  before,  but  as  a  rule  the  small 
segments  gave  values  of  supercooling  practically  the  same  as 
that  obtained  with  the  original  column  of  material. 

From  a  consideration  of  Tables  IV  to  IX  it  is  seen  that, 
with  very  few  exceptions,  the  contents  of  a  standard  tube 
solidified  at  a  temperature  above  that  at  which  the  contents 
of  the  capillary  tubes  solidified.  The  difference,  as  a  rule, 
was  considerable,  but  comparing  the  results  with  the  capillary 
tubes  with  each  other,  the  amount  of  supercooling  was  not 
always  the  same  for  tubes  of  equal  diameter,  even  when  the 
length  of  the  column  was  the  same.  The  readings  of  the 
standard  tubes  did  not  always  agree,  but  the  differences  here 
were  much  smaller  than  the  difference  between  the  results 
obtained  in  the  capillary  tubes.  It  is  also  evident  that  tubes 
of  widely  different  diameters,  but  within  what  we  may  call 
capillary  dimensions,  gave  practically  the  same  readings. 
Comparing  the  capillary  tubes  with  the  standard  tubes  it  is 
seen  that  the  increase  in  supercooling  is  not  proportional  to 


26 


Edward  A.  Rykenboer 


TABLE  IX 
Benzole  Acid.     M.  P.  =  121.4°  C 


Tube 
No. 

Mean 
Diam. 

Lg.  Col. 
in  mm 

S.  C.  i 

S.  C.   2 

S.C.3 

S.  C.  4 

S.  C.5 

in  mm 

174 

0.132 

5-3 

25.2 

36.9 

43-4 

— 

— 

164 

0.152 

2.0 

— 

41  .6 

49-o 

48.4 

49.9 

161 

o.  167 

6.6 

26.4 

46.6 

41-3 

41.4 

41.4 

175 

0.170 

2-5 

26.0 

21.6 

19.0 

— 

176 

0.179 

0.8 

39-9 

21-3 

13-4 

— 

— 

163 

o.  192 

5-2 

15-9 

19.4 

18.4 

18.4 

19.4 

1  68 

0.217 

6-5 

22.2 

3i-4 

14.9 

— 

— 

173 

0.235 

7.0 

32-8 

23.1 

38.4 

— 

— 

178 

0.262 

7-5 

19.4 

27.9 

32.4 

— 

— 

177 

0.265 

— 

40.6 

32.9 

24.4 

— 

— 

172 

0.276 

2.6 

27.2 

35-4 

32.9 

— 

— 

162 

0.281 

6.0 

28.2 

28.1 

32.3 

32.4 

32.4 

170 

0.308 

7-3 

24.4 

30-4 

24.4 

— 

— 

165 

0.311 

4-3 



31.2 

29.9 

37-4 

23.1 

169 

0-339 

2.6 

30-9 

34-8 

35-o 

— 

— 

1  60 

0-354 

6.8 

22.6 

41.4 

36.9 

32.9 

41.9 

171 

0-453 

2.6 

37-4 

35-2 

20.9 

— 

— 

167 

0.458 

2-3 

47-9 

33-4 

36.4 

— 

— 

179 

0.459 

2.2 

44-2 

32.9 

28.4 

— 

— 

159 

0-459 

II  .2 

10.6 

37-4 

37-4 

32.3 

39-6 

-       158 

0.894 

3-5 

21  .2 

3i-4 

41.4 

45-9 

16.4 

157 

4.1 

2-5 

9-3 

16.6 

12.4 

16.4 

13-4 

166 

4.4 

2.4 

7.6 

8-9 

8.9 

— 

— 

157  and  1  66  were  the  standard  tubes. 

the  decrease  in  diameter.     It  is  also  noticeable  that  the  super- 
cooling is  independent  of  the  length  of  the  enclosed  column 

of  material. 

Interpretation  of  Results 

It  is  reasonable  to  suppose  that  the  arrangement  of  mole- 
cules making  up  a  crystal  nucleus  is  characteristic  for  every 
substance  and  that  some  internal  molecular  configuration 
or  rearrangement  is  necessary  in  order  that  a  nucleus  may 
form.  It  may  be  some  such  arrangement  of  the  liquid  mole- 
cules as  given  by  A.  Johnson1  reasoning  from  the  work  of 
L,aue  and  the  Braggs  on  crystal  structure.  According  to 

1  Phys.  Zeit.,  16,  269  (1915). 


Capillary  Phenomena  and  Supercooling  27 

them,  a  crystal  must  have  minimal  symmetry;  i.  e.,  must  have 
one  and  only  one  of  the  230  Schoenflies  space  groups,  and  at 
the  same  time  it  must  conform  with  one  of  the  32  groups  of 
symmetry.  There  must  be  some  definite  arrangement  of 
the  liquid  molecules  or  atoms  which,  when  the  proper  con- 
ditions are  present,  give  rise  to  a  crystal  nucleus  or  center  of 
crystallization.  Now  as  the  temperature  of  the  substance 
is  lowered  below  the  melting  point,  crystallization  takes  place, 
but  in  materials  such  as  we  studied,  the  velocity  of  crystalliza- 
tion is  such  that  the  whole  mass  solidifies  rapidly  as  soon  as 
a  single  center  appears.  So  when  crystallization  occurred 
in  one  of  our  tubes  it  denoted  the  temperature  at  which  such 
a  center  first  appeared.  v  The  molecules  are  in  continuous 
motion  within  the  liquid  and  no  doubt  many  times  assume 
the  arrangement  necessary  for  the  formation  of  a  center,  but 
with  small  supercooling  the  viscosity  is  not  great  enough  to 
retard  the  motion  of  the  molecules  and  hold  them  in  that  po- 
sition long  enough  for  the  centers  to  form  and  to  allow  the 
crystallization  to  begin.  As  the  temperature  decreases  the 
viscosity  is  increased,  thereby  increasing  the  probability  of 
crystallization  until  a  maximum  of  probability  is  reached. 
Beyond  this  point  the  increased  viscosity  retards  the  forma- 
tion of  the  centers  or  is  so  great  that  the  internal  rearrangement 
is  hindered.  Then  if  the  temperature  could  be  lowered  enough 
without  having  a  center  form,  the  substance  could  be  obtained 
in  the  form  of  a  glass. 

The  number  of  centers  formed  spontaneously  depends  to 
a  large  extent  upon  the  volume  of  the  substance  considered, 
and  also  upon  the  inclination  of  the  curve  obtained  by  plotting 
the  number  of  crystal  centers  on  one  axis  and  the  correspond- 
ing temperature  on  the  other.  See  Figure  VI. 

If  the  number  of  centers  increases  rapidly  with  a  decrease 
in  temperature  the  conditions  would  be  represented  by  curve 
X,  but  if  the  number  of  centers  increases  slowly  with  a  decrease 
in  temperature,  curve  Y  would  represent  the  conditions. 
Curve  X  could  also  represent  the  number  of  centers  formed 
in  a  large  volume,  then  curve  Y  would  represent  the  conditions 


28 


Edward  A.  Rykenboer 


in  a  small  volume  of  the  same  substance.  Since  in  a  large 
volume  of  a  supercooled  liquid  the  number  of  centers  of  crystal- 
lization formed  at  any  given  temperature  is  greater  than  in 
a  small  volume  of  the  same  material,  the  probability  of  a  single 
center  being  formed  at  the  given  temperature  will  be  greater 
in  the  large  volume  than  in  the  small  one.  That  is  to  say,  if, 
in  a  certain  volume  there  appeared  four  centers  of  crystalliza- 
tion and  in  a  smaller  volume  only  one  appeared,  the  proba- 
bility of  just  one  center  forming  would  be  four  times  as  great 
in  the  larger  volume.  Let  a  point  where  such  a  center  appears 
be  represented  by  A  and  AI  on  the  curves  in  Figure  VI.  It 
is  seen  that  the  number  of  centers  formed  at  this  temperature 
is  about  four  times  greater  in  the  case  of  curve  X,  or  large 


Fig.  VI 

volume  curve,  than  for  curve  Y  or  curve  of  smaller  volume. 
In  order  to  have  equal  probability  for  both  cases  it  would 
be  necessary  to  pass  along  curve  Y  to  point  B.  Point  B  rep- 
resents the  same  number  of  centers  as  point  A,  and  hence  the 
probability  of  a  single  center  forming  would  be  the  same. 
But  point  B  is  at  a  much  lower  temperature  than  point  A  and 
consequently,  since  all  the  materials  used  crystallized  at  the 
appearance  of  the  first  center,  the  supercooling  in  the  case  of 
the  small  volume  would  be  much  greater.  If  the  volume  be- 
came very  small  the  probability  might  become  so  small  that 
not  even  one  center  would  even  appear  and  in  this  case  the 
liquid  would  remain  uncrystallized. 

If,  in  the  cases  cited  above,  the  number  of  centers  was 
very  small  even  in  a  large  volume,  the  temperature  might  be 


Capillary  Phenomena  and  Supercooling  29 

lowered  several  degrees  beyond  the  temperature  indicated 
by  the  probability  factor  before  crystallization  would  take 
place,  or  in  other  words,  before  a  center  would  appear.  The 
actual  appearance  of  a  center  might  then,  as  it  were,  lag 
behind  the  temperature  at  which  we  would  expect  it  to  appear. 
In  a  small  volume,  such  as  is  represented  by  a  capillary  tube, 
the  temperature  might  even  be  lowered  ten  or  fifteen  degrees 
beyond  the  point  indicated  by  the  probability  value,  before 
the  material  would  solidify.  This  would  allow  a  series  of  small, 
though  unequal  volumes,  to  give  values  of  supercooling  dis- 
tributed all  through  this  temperature  interval  and  explains, 
perhaps,  the  range  of  equal  readings  obtained  with  capillary 
tubes  of  different  diameters. 

The  fact  that  the  supercooling  was  not  proportional  to 
the  decrease  in  tube  diameter,  is  in  agreement  with  Tammann's 
observation,  that  the  decrease  in  the  number  of  crystal  nuclei 
was  much  greater  than  the  diminution  in  volume  seemed  to 
warrant,  and  it  supports  the  connection  that  we  have  attempted 
to  establish  between  the  supercooling  and  the  number  of  crystal 
nuclei. 

That  the  supercooling  was  apparently  independent  of. 
the  length  of  the  enclosed  column  of  material  seems  to  indi- 
cate that  perhaps  it  is  the  shape  of  the  supercooled  volume 
and  not  the  actual  volume  itself  that  is  the  determining  factor. 
Perhaps  the  arrangement  of  the  imaginary  units  of  volume 
with  respect  to  each  other  tends  to  aid  or  retard  the  formation 
of  crystal  nuclei.  It  is  conceivable  that  a  crystal  nucleus, 
to  form  and  to  grow,  needs  to  have  some  definite  quantity  of 
the  substance  all  around  it.  Then  for  any  volume,  a  spherical 
shape  would  give  the  largest  number  of  possible  centers,  and 
any  other  would  give  fewer.  In  the  discussion  above  then, 
perhaps  the  cross  section  of  the  various  tubes  should  be  con- 
sidered rather  than  the  corresponding  volumes. 

INFLUENCE  OF  VARIATION  IN  EXPERIMENTAL  METHOD 
Variation  in  Rate  of  Cooling" 

The  number  of  crystal  nuclei  formed  in  a  given  mass  is 
dependent  upon  the  time,  and  from  the  relation  established 


Edward  A.  Rykenboer 


between  the  number  of  crystal  nuclei  and  supercooling  (see 
Figure  VI)  we  would  expect  to  get  greater  supercooling  under 
conditions  of  more  rapid  cooling.  We  found,  however,  that 
the  rate  of  cooling  made  very  little  difference  in  the  amount  of 
supercooling  obtained,  as  can  be  seen  from  the  values  given 
in  Table  X. 

TABLE  X 
Sulphur    M.  P.  =  114-115°  C 


Tube 
No. 

Mean 
Diam. 
in  mm 

Lg.  Col. 
in  mm 

S.  C.  i 

S.  C.  2 

S.  C.  3 

S.  C.  4 

S.  C.  5 

61 

4.  10 

4-5 

32.5 

31-5 

27.9 

28.0 

27-7 

62 

0.917 

6.0 

45-o 

43-o 

45-5 

53-3 

48.5 

63 

0.214 

6-5 

50.8 

52.0 

52.5 

54-o 

53-6 

Heated  to 

140° 

140° 

n 

140 

140° 

140° 

Rate  of  Cooling 

slow 

slow 

fast 

fast 

fast 

61 

4.  10 

4-5 

34-5 

36.2 

41  .0 

36.5 

47.0 

62 

0.917 

6.0 

49-5 

55.8 

46.5 

46.5 

52.5 

63 

0.214 

6-5 

58.9 

61.7 

66.0 

61  .4 

62.0 

Heated  to 

155° 

155° 

170° 

170° 

170° 

Rate  of  Cooling 

fast 

slow 

slow 

slow 

fast 

Fast  Cooling  =  about  5  °  per  minute. 

Slow  Cooling  =  about  5°  in  10  minutes. 

The  rate  of  cooling  is  not  constant.  At  higher  tempera- 
tures it  is  more  rapid  than  at  lower  temperatures  but  the 
mean  values  above  are  close  enough.  The  difference  in  super- 
cooling under  the  different  conditions  of  cooling  from  any 
one  temperature  was  no  greater  than  the  difference  in  con- 
secutive readings  under  the  same  cooling  conditions. 

Variation  in  the  Material  of  Which  the  Tube  Is  Made 

The  point  of  solidification  is  mainly  a  function  of  the 
material  itself,  but  there  is  a  possibility  of  other  factors  in- 
fluencing the  crystallization  to  a  certain  extent.  For  example, 
different  supercooling  values  might  be  obtained  in  tubes  of 
glass  and  of  platinum  or  contact  with  different  substances 
might  help  or  hinder  supercooling.  Some  experiments  were 
carried  out  to  test  this  possibility,  using  acetanilide  as  the 
supercooled  material.  Two  glass  tubes  of  exactly  the  same 


Capillary  Phenomena  and  Supercooling 


diameter  and  from  the  same  piece  of  tubing,  containing  acetan- 
ilide,  were  heated  in  the  ordinary  manner  and  the  solidifying 
point  was  noted.  This  was  repeated  several  times  in  order 
to  increase  the  reliability  of  our  conclusions.  Strands  of  glass 
and  platinum  were  made  of  nearly  the  same  diameter.  The 
columns  of  acetanilide  in  the  capillaries  had  been  made  of  the 
same  length.  A  piece  of  the  glass  thread  was  put  in  one 
tube  and  a  piece  of  the  platinum  thread  was  put  in  the  other, 
and  they  were  long  enough  to  pass  through  the  acetanilide. 
The  heating  and  cooling  was  then  repeated  in  exactly  the  same 
way  as  before,  both  tubes  being  allowed  to  cool  at  the  same 
rate. 

TABLE  XI 
Acetanilide     M.  P.  =  112°  C.     Heated  to  120°  C 


Tube 
No. 

Mean 
Diam. 

Lg.  Col. 
in  mm 

Sub.  Added 

S.  C.  i 

S.  C.  2 

S.  C.  3 

S.  C.  4 

in  mm 

X 

0.411 





45-4 

42.0 

45-7 



Y 

0.411 

— 

— 

45-3 

45-2 

44.8 

— 

X 

0.411 

5-2 

Platinum 

41  .0 

43-6 

42.1 

41-5 

Y 

0.411 

5-2 

Glass 

41.7 

44.8 

44.0 

43-5 

Diameter  of  Strands — Platinum  =  0.121  mm.  Glass  =  0.116 
mm. 

The  slight  difference  noted  in  the  supercooling  with 
the  threads  was  practically  the  same  as  the  difference  between 
the  successive  readings  of  the  tubes  without  them.  These 
experiments  led  us  to  conclude  that  the  nature  of  the  surface 
in  contact  with  the  crystallizing  liquid  does  not  influence  the 
temperature  at  which  crystallization  begins. 

That  a  difference  in  the  surface  tension  between  the 
large  and  small  tubes  would  account  for  the  difference  in  super- 
cooling hardly  seems  plausible  since  the  difference  in  surface 
tension  must  be  very  slight.  G.  Quincke's1  experiments 
seem  to  show  that  the  difference  between  the  surface 
tensions  in  tubes  of  different  diameters  is  slight  and  that  the 
surface  tension  is  greater  in  larger  tubes.  The  experiments 

1  Wied.  Ann.,  52,  1-22  (1894). 


32  Edward  A.  Rykenboer 

of  P.  Volkmann,1  however,  indicate  that  the  surface  tension 
is  smaller  in  larger  tubes,  but  his  experiments  also  show  only 
slight  differences  between  the  surface  tension  values. 

If  in  the  tubes  there  were  any  relation  between  the  sur- 
face tension  and  the  supercooling  obtainable,  there  ought  to 
be  some  relation  between  the  position  of  the  center  of  crystal- 
lization and  the  surface.  No  such  relationship  could  be  found, 
the  contents  of  the  tubes  beginning  to  solidify  at  times  in  the 
interior  and  at  other  times,  perhaps,  in  .the  surface  layer. 
If  a  change  in  the  surface  tension  changed  the  amount  of 
supercooling  obtainable,  it  would  be  reasonable  to  expect  a 
gradual,  continuous  change  in  the  amount  of  the  supercool- 
ing, increasing  or  decreasing  as  the  diameters  of  the  capil- 
laries were  varied.  No  evidence  of  this  sort  is  perceptible 
in  any  of  the  tables.  Some  of  the  capillary  tubes  gave  nearly 
the  same  values  of  supercooling  as  the  standard  tubes,  while 
others  of  almost  the  same  size  gave  much  greater  values. 

PART  II— EFFECT  UPON  THE  SUPERCOOLING  OF  THE 

MOLECULAR  AGGREGATION  OF  THE  MATERIAL 

IN  THE  LIQUID  STATE 

Introduction 

Since  we  believe  that  the  formation  of  a  crystal  nucleus 
is  due  to  a  definite  molecular  configuration  within  the  liquid, 
we  would  naturally  expect  to  have  a  change  in  the  character 
and  number  of  nuclei  if  the  molecular  arrangement  in  the 
liquid  were  changed.  This  would  undoubtedly  involve  a 
change  in  the  supercooling  values  also.  In  fact,  we  could 
detect  such  a  change  in  the  liquid  by  observing  changes  in 
the  values  of  supercooling.  Such  a  transformation  or  re- 
arrangement could  be  brought  about  in  several  ways  but  we 
shall  confine  ourselves  to  a  study  of  the  effect  of  variation 
in  the  temperature  to  which  the  material  is  heated.  Sulphur 
has  proved  itself  to  be  an  ideal  substance  for  this  purpose  and 
a  review  of  the  changes  brought  about  in  the  liquid  sulphur 


1  Wied.  Ann.,  53   633-663,  664-666  (1894). 


Capillary  Phenomena  and  Supercooling  33 

by  changes  in  temperature  is  necessary  before  our  experimental 
results  can  be  interpreted. 

Chemistry  of  Molten  Sulphur 

The  effect  of  the  temperature  to  which  liquid  sulphur 
has  been  heated,  has  been  the  subject  of  a  large  amount  of 
work.  D.  Gernez1,  by  making  use  of  the  inoculation  method 
for  determining  the  freezing  point,  found  that  the  freezing  point 
of  sulphur  is  not  constant,  but  depends  upon  the  temperature 
to  which  it  has  been  heated.  He  found  that  when  sulphur 
was  fused  at  121  °  C  and  cooled,  the  freezing  point  was  117.4°. 
When  the  liquid  was -heated  to  144°  it  had  a  freezing  point 
of  113.4°  and  when  kept  at  170°  for  five  minutes  the  freezing 
point  fell  to  112.2°.  Later  he  found2  by  heating  sulphur  to 
1 60°,  then  allowing  it  to  cool  to  100°  and  holding  it  there  for 
some  time,  that  when  the  sides  of  the  containing  vessel  were 
rubbed,  a  deposition  of  "pearly"  sulphur  was  obtained. 
Smith  and  Carson3  represented  this  pearly  or  nacreous  forma- 
tion by  Sin  orthorhombic  by  Si  and  monoclinic  by  Sn. 
They  found  that  the  liquid  from  which  the  nacreous  modi- 
fication has  been  separated  may  be  converted  into  mono- 
clinic  or  orthorhombic  sulphur  by  the  touch  of  a  correspond- 
ing crystal.  In  the  conversion  of  liquid  to  ordinary  crystals 
in  this  way,  the  reaction  takes  place  with  seven-fold  rapidity 
after  the  nacreous  crystals  have  been  deposited,  and  Gernez 
considers  that  at  the  temperature  of  160°  the  allotropic  pearly 
modification  is  produced,  and  by  its  solution  in  the  rest  of  the 
liquid  the  latter  is  in  the  condition  of  a  supersaturated  solu- 
tion. F.  W.  Kuster4  found  that  the  amount  of  insoluble 
sulphur  present  after  solidification  was  dependent  only  upon 
the  rate  of  crystallization  and  the  temperature  at  which  the 
crystallization  occurred,  and  not  upon  the  temperature  to 
which  it  had  been  heated  nor  upon  the  length  of  time  of  heat- 
ing. He  concludes  that  the  soluble  and  insoluble  forms  of 


1  Comptes  rendus,  82,  1151  (1876);  Phil.  Mag.,  [5]  2,  79  (1876). 

2  Comptus  rendus,  98,  144  (1884). 

3  Zeit.  phys.  Chem.,  71,  661-676  (1911). 

4  Zeit.  anorg.  Chem.,  18,  365  (1898). 


34  Edward  A.  Rykenboer 

sulphur  are  isomerides.  Other  experimenters,  however,  seem 
to  agree  that  the  insoluble  variety  of  sulphur  is  present  in 
increasing  amounts  as  the  temperature  is  raised  above  the 
melting  point.  P.  Duhem1  explains  the  difference  in  velocity 
of  crystallization  of  sulphur  as  due  to  the  difference  in  con- 
centration of  the  insoluble  form.  Alexander  Smith2  found  that 
the  formation  of  insoluble  sulphur  takes  place  in  an  irregular 
manner  as  the  temperature  is  raised  above  the  melting  point 
and  that  the  depression  of  the  freezing  point  is  proportional 
to  the  amount  of  insoluble  sulphur  thus  formed.  In  a  later 
investigation3  he  found  that  yellow  mobile  sulphur  (Sx) 
predominates  from  the  melting  point  to  160°  and  that  the 
brown  viscous  or  amorphous  (insoluble)  sulphur  (SM)  in- 
creases greatly  in  amount  above  160°  at  the  expense  of  S\. 
He  thought  that  this  indicated  a  transition  point,  since  a 
separation  into  the  two  phases,  yellow  and  brown  liquid 
sulphur,  was  observed.4  Later,  however,  he5  accepted  the 
view  of  Hoffman  and  Rothe6  that  there  is  no  transition  point 
in  the  ordinary  sense,  for  if  the  rate  of  cooling  was  diminished 
the  discontinuity  did  not  appear  and  therefore  the  two  modifi- 
cations must,  under  ordinary  conditions,  be  completely  miscible 
with  each  other.  The  apparent  separation  into  two  phases 
was  brought  about  by  the  differences  in  temperature  which 
arise  in  a  column  of  the  liquid  owing  to  the  poor  conduction 
of  heat,  in  reality  there  being  no  formation  of  two  phases, 
the  difference  in  color  being  accounted  for  by  the  difference 
in  temperature.  Smits  and  Leuw7  apparently  accepted  these 
views  also  since  they  found  that  the  liquid  sulphur  contains 
the  two  forms  S\  and  SM  in  equilibrium  proportions. 


1  Zeit.  phys.  Chem.,  23,  193-266  (1897). 

2  Ibid.,  42,  469  (1903);  Proc.  Roy.  Soc.  Edin.,  24,  299,  342  (1902). 

3  Proc.  Roy.  Soc.  Edin.,  25,  588  (1905). 

4  Jour.  Am.  Chem.  Soc.,  27,  797-820  (1905). 

6  Proc.  Roy.  Soc.  Edin.,  26,  352  (1906);  Zeit.  phys.  Chem.,  59,  448  (190?); 
Jour.  Am.  Chem.  Soc.,  29,  499  (1907). 

6  Zeit.  phys.  Chem.,  55,  113-124  (1906). 

7  Proc.  Akad.  Wetensch.  Amsterdam,  14,  461  (1911);  Zeit.  phys.  Chem., 
83,  221-241  (1913)- 


Capillary  Phenomena  and  Supercooling  35 

In  addition  to  Sx  and  SM,  A.  H.  Aten1  has  described 
two  other  forms  of  sulphur,  ST  and  S*.  S^  is  not  formed, 
however,  by  the  action  of  heat  upon  sulphur  and  is  of  no 
interest  to  us.  Sw  is  formed  when  sulphur  is  heated  above 
its  melting  point  and  then  is  rapidly  cooled.  The  relative 
quantities  of  Sx,  SM  and  ST  present  in  sulphur  which  has  been 
heated  to  various  temperatures  have  been  determined  by 
Aten.2  The  amount  of  ST  is  at  a  maximum  when  the  sulphur 
has  been  heated  to  180°  and  at  this  point  the  amount  present 
is  6.5%.  The  quantity  of  SM  increases  as  the  temperature 
rises  to  448°  C,  the  greatest  rate  of  increase  being  between 
170°  and  1 80°.  Sx  decreases  as  the  temperature  increases. 
He  gives  the  composition  at  180°  as  S»  =  6.5  percent,  SM  = 
20.4  percent  and  Sx  =  73.1  percent. 

Summarizing  all  this:  when  sulphur  is  heated  to  various 
temperatures  above  its  melting  point  there  are  present  prin- 
cipally the  four  modification  ST,  SM,  ST  and  Sm.  Sx  is  soluble 
sulphur  and  is  present  in  the  greatest  amounts,  decreasing, 
however,  with  increase  of  temperature  above  the  melting  point. 
SM  is  insoluble  or  amorphous  sulphur  which  increases  in  amount 
as  the  temperature  is  raised  with  the  maximum  rate  of  increase 
between  170°  C  and  180°.  ST  is  present  in  small  amounts 
but  increases  to  a  maximum  as  the  temperature  is  raised  to 
1 80°  and  then  decreases.  Sm  or  pearly  sulphur,  begins  to 
form  at  160°  C.  The  various  forms  of  sulphur  occurring  to- 
gether in  the  liquid  state  are  mutually  miscible. 

Influence  of  Foreign  Material  upon  the  Formation  of 
Crystallization  Nuclei 

Tammann3  has  observed  that  the  addition  of  soluble 
materials  to  a  supercooled  liquid  causes  a  decided  change  in 
the  number  of  crystal  centers  and  in  the  temperature  at  which 
a  maximum  number  forms  per  unit  time.  By  the  addition 
of  one  substance  the  temperature  for  maximum  number  of 


1  Zeit.  phys.  Chem.,  81,  257-280  (1912);  88,  321-379  (1914)- 

2  Ibid.,  86,  1-35  (1913). 

3  Ibid.,  25   453  (1898). 


36  Edward  A.  Rykenboer 

centers  was  lowered  while  the  addition  of  another  substance 
would  cause  a  shift  towards  higher  temperatures.  In  some 
cases  the  maximum  point  was  at  the  same  temperature  but 
the  number  of  centers  was  changed,  with  some  added  materials 
the  number  being  larger,  and  with  others,  it  was  smaller.  Of 
course  this  caused  a  decided  change  in  the  slope  of  the  curve. 
We  have  indicated  the  relation  between  the  number  of  crystal 
nuclei  and  supercooling  and  have  also  shown  the  effect  of  the 
slope  of  the  curve  representing  the  variation  in  number  of 
crystal  centers  with  temperature.  It  would  seem,  then,  that 
added  foreign  materials  would  cause  a  change  in  supercooling, 
either  increasing  it  or  decreasing  it  as  the  case  may  be. 

As  sulphur  is  heated  to  various  temperatures  above  its 
melting  point,  increasing  amounts  of  new  and  in  that  sense 
foreign  materials  are  formed  as  has  just  been  described, 
consequently  a  shifting  of  the  curve  representing  the  number 
of  crystal  nuclei  could  be  expected.  Since  the  amount  of 
supercooling  in  capillary  tubes  depends  upon  the  position  of 
the  maximum  and  the  slope  of  the  nuclei  curve,  any  such  shifting 
would  be  indicated  by  a  change  in  the  amount  of  supercooling 
obtained. 

Method  and  Results 

The  degrees  of  supercooling  of  sulphur  when  cooled  from 
temperatures  just  above  its  melting  point  have  been  given. 
When  it  was  heated  to  points  between  120°  and  200°,  changes 
in  the  supercooling  values  with  the  capillary  tubes  were  ob- 
served. The  heating  was  carried  on  in  the  usual  way.  Both 
rapid  and  slow  cooling  was  tried  with  no  noticeable  difference 
in  the  results.  Table  XII  shows  the  effect  of  heating  to  diff- 
erent temperatures  upon  the  amount  of  supercooling  after- 
ward obtained,  and  it  also  shows  that  whether  the  cooling  is 
fast  or  slow  the  results  are  practically  the  same. 

In  obtaining  the  results  given  in  Table  XII  the  tubes 
were  first  allowed  to  cool  slowly  from  the  temperature  given 
in  the  table  and  then  the  time  of  cooling  was  shortened 
for  the  same  tubes  from  the  same  temperature  point.  The 
fast  cooling  was  about  12°  per  minute  while  the  slow  cooling 


Capillary  Phenomena  and  Supercooling 


37 


TABUS  XII 

Sulphur    M.  P.  =  114-115°  C 

Cool  =  Rate  of  Cooling      Heat  =  Temperature  to  which  Substance 

was  heated 


Tube  No. 

Mean  Diam. 
in  mm 

Lg.  Col. 
in  mm 

61 

4.  10 

4-5 

62 

0.917 

6.0 

63 

0.214 

6-5 

Tube  No. 

S.  C.  i 

S.   C.   2 

S.  C.  3 

S.  C.  4 

S.  C.  5 

61 

30-4 

31.0 

27-5 

28.5 

30.0 

62 

36.0 

47.0 

47-3 

46.5 

50.2 

63 

37-8 

4i-5 

54-4 

42.5 

53-0 

Cool 

slow 

slow 

slow 

slow 

fast 

Heat 

125° 

125°' 

125° 

125° 

125° 

61 

32.5 

31-5 

27.9 

28.0 

27-7 

62 

45-o 

43-o 

45-5 

53-3 

48.5 

63 

50.8 

52.0 

52.5 

54-o 

53-6 

Cool 

slow 

slow 

fast 

fast 

fast 

Heat 

140° 

140° 

n 

140 

140° 

140° 

61 

34-5 

36.2 

62 

49-5 

55-8 

63     . 

58-9 

61.7 

Cool 

fast 

slow 

Heat 

155° 

155° 

Tube  No. 

S.  C.  i 

S.   C.   2 

S.  C.  3 

S.  C.4 

S.  C.  5 

S.  C.  6 

S.  C.  7 

S.C.8 

61 

34-o 

34-5 

37-o 

43-5 

44.2 

42.0 

46.0 

44-5 

62 

45-5 

44-5 

45-5 

51.0 

50-5 

45-5 

50-5 

56.0 

63 

93-o 

92.5 

80.0 

66.0 

86.0 

80.0 

76.0 

80.0 

Cool 

slow 

slow 

slow 

fast 

fast 

fast 

fast 

fast 

Heat 

170° 

170° 

170° 

170° 

170° 

170° 

170° 

170° 

Tube  No. 

S.  C.  i 

S.   C.   2 

Tube  No. 

S.  C.  i 

S.  C.  2 

61 

62 

63 
Cool 

38.3 
48.0 

75-o 
slow 

41  .0 
48.0 

75-5 
fast 

61 
62 

63 
Cool 

33-5 
48.0 

59-5 
slow 

42.0 

56.2 

66.2 
fast 

Heat 

190° 

190° 

Heat 

225° 

225° 

Edward  A.  Rykenboer 


Tube  No. 

S.  C.  i 

S.   C.   2 

Tube  No. 

S.  C.  i 

61 

41  .0 

36.5 

61 

47.0 

62 

46.5 

46.5 

62 

52.5 

63 

60.0 

61  .4 

63 

62.0 

Cool 

slow 

slow 

Cool 

fast 

Heat 

170° 

i7o° 

Heat 

225° 

was  about  1.2°  to  2°  per  minute.  This  was  repeated  at  each 
successive  elevation  of  the  temperature  to  which  the  heating 
was  carried,  but  as  can  be  seen  from  the  table,  no  great  change 
in  the  supercooling  was  observed.  At  about  170°  a  decided 
change  was  noticed  in  the  readings  with  the  smallest  tube  63. 
The  largest  tube  61  did  not  show  such  a  large  change  and 
the  intermediate  tube  62  gave  values  between  those  of  the 
other  two.  Tubes  of  practically  the  same  diameter  gave 
wide  variations,  as  subsequent  data  will  show,  but  as  a  rule 
the  values  of  supercooling  were  larger  than  those  given  by  this 
tube  62.  When  the  heating  was  carried  to  about  225  °,  smaller 
values  were  again  obtained  which  persisted  even  when  the 
tubes  were  reheated  to  170°,  the  temperature  corresponding 
to  the  maximum  supercooling.  It  may  be  inferred  that  the 
modification  which  formed  at  170°  was  permanent  since  a 
tube  heated  to  that  temperature  and  cooled  gave  the  same 
value  when  reheated  to  125  °  and  cooled  at  the  same  rate. 

With  the  ordinary  supercooling  of  sulphur  from  its  melting 
point  the  whole  mass  solidified  in  an  instant  as  soon  as  the 
first  center  appeared,  but  where  the  supercooling  was  carried 
to  room  temperature  before  a  center  appeared  the  rate  of 
crystallization  was  decidedly  slow  and  the  solidification  of 
the  mass  continued  to  grow  from  the  first  center  formed  while 
the  temperature  was  lowered  perhaps  ten  degrees  in  five  min- 
utes. The  fact  that  no  more  centers '  formed  even  when  the 
tube  was  so  slowly  cooled  through  ten  degrees,  seems  to  point 
to  a  small  number  of  centers  even  at  the  maximum  point. 

A  graphical  representation  of  the  data  in  Table  XII  is 
given  in  Fig.  VII.  The  horizontal  axis  represents  the  de- 


Capillary  Phenomena  and  Supercooling 


39 


grees  of  supercooling  and  the  vertical  axis  shows  the  tempera- 
ture to  which  the  heating  was  carried  before  the  supercooling 
was  measured.  Points  on  the  curves  represent  average  values. 
Although  Curve  B  crosses  Curve  C  at  the  lowest  preheating 
temperature  used,  it  is  evident  that  it  follows  the  contour  of 
the  curve  for  the  standard  tube  for  its  whole  length,  and  this 
might  be  expected  since  the  tube  is  hardly  of  capillary  di- 
ameter. 


O*      //?'       24°     36°      4Sn      60°       72° 


Fig.  VII 


In  order  to  show  that  the  change  at  170°  was  permanent 
a  series  of  capillary  tubes  were  heated  to  170°,  then  cooled 
to  1 00°  and  held  there  for  five  hours.  The  supercooling 
values  were  then  determined  and  they  corresponded  to  those 
obtained  without  this  long  wait,  instead  of  to  those  'obtained 
after  heating  only  to  a  lower  temperature.  The  tubes  were 
again  heated  to  170°  and  this  time  cooled  to  75°  and  held  at 
this  temperature  for  several  hours.  The  .results  were  similar 


Edward  A.  Rykenboer 


to  those  obtained  when  the  wait  was  at  100°.  If  the  change 
within  the  liquid  had  not  been  permanent  it  would  surely 
have  reversed  itself  to  at  least  some  extent,  during  these  long 
waits.  The  experimentally  observed  values  are  given  in  Table 
XIII. 

TABUS  XIII 
Sulphur 


Tube  No. 

Mean  Diam. 
in  mm 

Lg.  Col. 

in  mm 

S.  C.  i 

S.  C.   2 

S.C.3 

S.C.4 

219 

o.  191 

5-6 

55-0 

64.0 

51.0 

58.7 

222 

0.205 

4-3 

55-5 

87.5 

83-0 

78-5 

218 

0.2II 

4.2 

43-8 

70.0 

72.5 

73-7 

2I7 

0.237 

5-2 

44.0 

88.0 

71.0 

75-9 

214 

0.252 

5-5 

44.0 

59-4 

59-0 

56.3. 

213 

0.267 

5-7 

59-o 

83-0 

81.0 

79.0 

215 

0.271 

6-5 

53-o 

64.5 

76.5 

77-5 

216 

0.276 

5-2 

48.0 

78.5 

70.5 

71.0 

212 

0.321 

3-9 

41  .0 

48.5 

70.8 

74.0 

211 

0-339 

4.8 

47.0 

56.0 

58.0 

55-o 

210 

0.429 

3-5 

50.7 

— 

71.0 

69.0 

Temp,  heated  to 

125° 

185° 

185° 

i85° 

After  the  readings  S.  C.  2  were  taken,  the  sulphur  was  heated 
to  185°.  It  was  then  cooled  to  100°  and  held  at  this  point 
for  five  hours  and  then  cooled  as  usual  giving  the  readings 
in  S.  C.  3.  This  procedure  was  repeated  for  the  values  in  the 
column  headed  S.  C.  4  except  that  the  temperature  was  first 
lowered  to  75  °  and  held  here  for  five  hours.  It  was  then  cooled 
as  usual  giving  the  readings  in  S.  C.  4. 

Table  XIV  gives  more  data  of  the  same  kind  as  that  in 
Table  XIII  and  confirms  further  our  belief  that  holding  the 
temperature  constant  at  a  point  far  below  the  temperature 
where  we  presume  a  permanent  transformation  took  place, 
is  without  effect  in  reversing  the  transformation. 


Capillary  Phenomena  and  Supercooling 


TABLE  XIV 
Sulphur 


Tube  No. 

Mean  Diam. 
in  mm 

Lg.  Col. 
in  mm 

S.  C.  i 

S.  C.   2 

S.  C.  3 

206 

O.2OI 

4-7 

84-5 

91  .0 

100.  0 

2OI 

0.220 

5-6 

68.5 

58.0 

55-0 

205 

0.238 

5-8 

68.0 

82.5 

81.5 

204 

0.272 

3-5 

69.0 

83.0 

89.2 

203 

0.281 

4.0 

88.5 

74.0 

95-5 

202 

0.284 

4.0 

59-o 

64.0 

82.0 

I98 

0.470 

8.2 

68.0 

64.5 

73-o 

199 

0-655 

5-4 

67.0 

62.0 

60.0 

Temp,  heated  to 

190° 

185° 

185° 

After  the  readings  S.  C.  2  were  taken  the  sulphur  was  heated 
to  185°.  It  was  then  cooled  to  100°  and  held  at  this  point 
for  three  hours  and  then  cooled  as  usual,  giving  the  readings 

in  S.  C.  3. 

Interpretation  of  Results 

The  greatly  increased  supercooling  obtained  with  capillary 
tubes  after  heating  to  170°  or  above  indicates  a  broad  shifting 
of  the  crystallization  center  curve  towards  lower  tempera- 
tures. The  probable  change  is  indicated  in  Fig.  VIII. 


of  scsfxtrcoohnq 

Fig.  VIII 

The  effect  of  added  materials  upon  the  position  and  char- 
acter of  the  nuclei  curve  has  already  been  discussed.  In 
Fig.  VIII  the  added  materials  are  the  various  forms  of  sul- 
phur formed  by  the  action  of  heat  at  temperatures  above  the 
melting  point.  Curve  X  represents  the  conditions  in  liquid 


42  Edward  A.  Rykenboer 

sulphur  which  has  been  heated  only  to  the  melting  point  and 
Curve  Xi  represents  conditions  resulting  from  heating  to  170° 
C.  The  two  curves  start  to  leave  the  horizontal  axis  at 
approximately  the  same  point  since  the  change  in  supercooling 
values  for  the  standard  tube  is  very  small.  As  has  been  said, 
in  a  large  volume  such  as  in  a  standard  tube,  a  center  of  crys- 
tallization will  appear  practically  as  soon  as  suitable  conditions 
are  present,  and  this  would  be  where  the  curve  starts  to  leave 
the  temperature  axis.  The  maximum  value  for  Curve  Xi  is 
below  that  for  Curve  X  since  we  have  found  that  the  number 
of  centers  formed  in  sulphur  that  has  been  heated  to  170° 
is  smaller  than  when  it  is  heated  only  to  the  melting  point. 
The  maximum  point  will  also  be  farther  along  the  temperature 
axis  for  Curve  Xi  since  the  increase  in  supercooling  for  the 
capillary  tubes  is  very  large.  With  a  lower  maximum  point 
shifted  to  the  right,  Curve  Xi  will  have  a  more  gentle  slope 
than  Curve  X. 

The  point  of  crystallization  for  the  standard  tubes  is 
represented  by  O  and  d  the  projections  of  which  upon  the 
horizontal  axis  give  the  temperature  readings  A  and  AI. 
P  represents  the  point  where  sulphur  in  a  capillary  tube, 
that  has  been  heated  only  to  the  melting  point,  will  crys- 
tallize out,  the  increased  elevation  of  the  point  counterbalancing 
the  decreased  volume.  Thus  P  and  O  would  represent  equal 
probability  of .  crystallization.  Point  PI  represents  the  crys- 
tallization point  for  the  same  tube  after  it  has  been  heated 
to  170°.  Equal  elevation  for  the  same  volume  indicates  equal 
probability  for  the  formation  of  a  crystal  nucleus.  But  in 
the  case  of  PI  the  temperature  is  lower,  which  corresponds 
to  greater  supercooling. 

Let  us  assume  that  SM  and  ST  have  a  combined  effect  in 
shifting  the  curve  of  crystal  centers  to  the  right  in  Fig.  VIII. 
The  increase  in  supercooling  indicated  by  the  gradual  rise  of 
Curve  C  in  Fig.  VII  would  then  be  attributed  to  the  gradual 
formation  of  SM  and  S,.  In  the  neighborhood  of  160°  the 
rate  of  formation  of  SM  suddenly  increases  and  this  is  indicated 
by  the  bend  in  the  curve  at  S  continuing  to  V.  The  influence 


Capillary  Phenomena  and  Supercooling  43 

of  S,r  now  grows  less  since  the  maximum  percentage  comes 
at  170°  and  simultaneously  Sm  or  nacreous  sulphur  is  formed. 
If  we  assume  that  the  addition  of  Sm  to  the  fused  mass  causes 
the  curve  to  shift  in  the  same  direction  as  does  SM  and  ST 
then  there  will  be  no  decided  break  in  the  curve  but  the  curve 
will  continue  to  rise  more  gradually  to  the  right,  the  increas- 
ing amounts  of  Sm  partially  making  up  for  the  decreased  rate 
of  formation  of  SM  and  ST.  Apparently,  however,  Sm  at 
temperatures  above  170°  exerts  an  opposite  and  stronger 
effect  than  does  SM  for  there  is  a  sharp  bend  in  the  curve  at 
170°  and  above  this  temperature  it  gradually  approaches  the 
vertical  axis.  The  corresponding  Curve  A  for  the  standard 
tube  shows  the  same  effect  but  less  pronounced. 

Conclusions 

We  have  designed  a  form  of  apparatus  for  the  measure- 
ment of  supercooling  in  capillary  tubes. 

We  have  shown  that  decidedly  greater  supercooling  can 
be  produced  in  capillary  tubes  than  in  tubes  of  larger  diameter. 

We  did  not  succeed  in  formulating  a  mathematical  con- 
nection between  the  amount  of  supercooling  obtainable  and 
the  diameter  of  the  capillary. 

We  have  developed  a  plausible  explanation  for  the  in- 
crease in  supercooling  found  possible  in  capillary  tubes. 

We  have  obtained  evidence  indicating  that  the  material 
of  the  tube  has  little  if  any  effect  on  the  degree  of  supercooling, 
and  have  reached  the  conclusion  that  small  changes  in  surface 
tension  are  likewise  of  insignificant  importance. 

We  have  found  that  in  the  case  of  sulphur,  the  amount  of 
supercooling  depends  upon  the  temperature  to  which  the 
substance  was  heated  previously. 

We  have  offered  a  plausible  explanation  of  this  interesting 
phenomenon. 


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